ieq-05global positioning system notes

8/8/2019 IEQ-05Global Positioning System Notes

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Course TitleIEQ-05 Earthquake Geology and Geoinformatics

(Dept. of Earthquake Engineering, IIT Roorkee)

Global Positioning System (GPS)

What is the GPS?

Orbiting navigational satellites

– Transmit position and time data Handheld receivers calculate

– latitude

– longitude

– altitude

– velocity Developed by Department of Defense (Billions and billions of dollars have been

invested in creating this technology for military uses).

Components of the System

Space segment 24 satellite vehicles Six orbital planes

– Inclined 55o

with respect to equator

– Orbits separated by 60o

20,200 km elevation above Earth Orbital period of 11 hr 55 min Five to eight satellites visible from any point on Earth

Block I Satellite Vehicle

G P S

The GPS satellites orbit the earth in 12 hours. There are often more than 24operational satellites as new ones are launched to replace older satellites.The satellite orbits repeat almost the same ground track (as the earth turns beneaththem) once each day.The orbit altitude is such that the satellites repeat the same track and configuration over

any point approximately each 24 hours (4 minutes earlier each day).This constellation provides the user with between five and eight SVs visible from anypoint on the earth.

GPS satellites are orbited high enough to avoid the problems associated with land basedsystems, yet can provide accurate positioning 24 hours a day, anywhere in the world.Uncorrected positions determined from GPS satellite signals produce accuracies in therange of 50 to 100 meters. When using a technique called differential correction, users can



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get positions accurate to within 5 meters or less. GPS has found its greatest utility in thefield of Geographic Information Systems (GIS).

With some consideration for error, GPS can provide any point on earth with a uniqueaddress (its precise location). A GIS is basically a descriptive database of the earth (or aspecific part of the earth). GPS tells you that you are at point X,Y,Z while GIS tells youthat X,Y,Z is a monument, or a spot in a region. GPS tells us the "where“ and GIS tells us

the "what". GPS/GIS is reshaping the way we locate, organize, analyze and map ourresources.

How GPS Determines a Location

Trilateration process.

GPS is based on satellite ranging - calculating the distances between the receiver andthe position of 3 or more satellites (4 or more if elevation is desired) and then applyingsome mathematics.

Accurate timing is the key to measuring distance to satellites. Satellites are accuratebecause they have four atomic clocks ($100,000 each) on board. Extra satellite rangemeasurement can remove errors if any.

Assuming the positions of the satellites are known, the location of the receiver can becalculated by determining the distance from each of the satellites to the receiver.GPS takes these 3 or more known references and measured distances and"TRIANGULATES" an additional position.

Measuring Distance

Distance = Velocity * Time – Velocity is that of a radio wave.

– Time is the travel time of the signal.Measure the travel time

– Receiver generates the same codes as the satellite (Pseudo Random Noise-PRN codes).

– Measure delay between incoming codes and self generated codes.

– D = Speed of light * measured delay.

Distance = Time Delay * Speed of light

Signal Generated at Satellite



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Signal generated at satellite

Received Signal

Receiver generated signal with phase delay

Signal generated by receiver

Triangulation in 2D

If location of point A is known, and the distance to point A is known, desiredposition lies somewhere on a circle. Could be anywhere along the circle.

Distance to two points are known. Desired position is in one of two locations. Distance to three points are known. Position is known!

Triangulation in 3D Distance to 3 points are known. Intersects at 2 points.

How the Current Locations of GPS Satellites are Determined

GPS satellites are orbiting the Earth at an altitude of 20,200 km. The DOD can predict thepaths of the satellites vs. time with great accuracy. Furthermore, the satellites can beperiodically adjusted by huge land-based radar systems. Therefore, the orbits, and thus the



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locations of the satellites, are known in advance. Today's GPS receivers store this orbitinformation for all of the GPS satellites in what is known as an almanac. Think of thealmanac as a "bus schedule" advising you of where each satellite will be at a particulartime. Each GPS satellite continually broadcasts the almanac.Your GPS receiver will automatically collect this information and store it for futurereference. The Department of Defense constantly monitors the orbit of the satelliteslooking for deviations from predicted values. Any deviations (caused by natural

atmospheric phenomenon such as gravity), are known as ephemeris errors. Whenephemeris errors are determined to exist for a satellite, the errors are sent back up to thatsatellite, which in turn broadcasts the errors as part of the standard message, supplying thisinformation to the GPS receivers. By using the information from the almanac inconjunction with the ephemeris error data, the position of a GPS satellite can be veryprecisely determined for a given time.

Computing Distance Between GPS Satellites & Receiver

GPS determines distance between a GPS satellite and a GPS receiver by measuring theamount of time it takes a radio signal (the GPS signal) to travel from the satellite to the

receiver. Radio waves travel at the speed of light, which is about 186,000 miles persecond. So, if the amount of time it takes for the signal to travel from the satellite to thereceiver is known, the distance from the satellite to the receiver (distance = speed x time)can be determined. If the exact time when the signal was transmitted and the exact timewhen it was received are known, the signal's travel time can be determined.

In order to do this, the satellites and the receivers use very accurate clocks which aresynchronized so that they generate the same code at exactly the same time. The codereceived from the satellite can be compared with the code generated by the receiver. Bycomparing the codes, the time difference between when the satellite generated the code andwhen the receiver generated the code can be determined. This interval is the travel time of

the code. Multiplying this travel time, in seconds, by 186,000 miles per second gives thedistance from the receiver position to the satellite in miles.

Four Satellites to give a 3D position

Therefore, a fourth variable (in addition to x, y and z), time, must be determined in order tocalculate a precise location. Mathematically, to solve for four unknowns (x, y, z, and t),there must be four equations.

Measuring GPS Accuracy

Major factor in determining positional accuracy is the alignment, or geometry, of the groupof satellites (constellation) from which signals are being received. The geometry of theconstellation is evaluated for several factors, all of which fall into the category of Dilution

Of Precision, or DOP. DOP is an indicator of the quality of the geometry of the satelliteconstellation. Your computed position can vary depending on which satellites you use forthe measurement. Different satellite geometries can magnify or lessen the errors in theerror budget described above. A greater angle between the satellites lowers the DOP, andprovides a better measurement. A higher DOP indicates poor satellite geometry, and aninferior measurement cofiguration.



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Good Satellite Geometry Poor Satellite Geometry

Some GPS receivers can analyze the positions of the satellites available, based upon thealmanac, and choose those satellites with the best geometry in order to make the DOP aslow as possible. Another important GPS receiver feature is to be able to ignore or eliminateGPS readings with DOP values that exceed user-defined limits.

Other GPS receivers may have the ability to use all of the satellites in view, thusminimizing the DOP as much as possible.

Differential GPS to Increase Accuracy

A technique called differential correction is necessary to get accuracies within 1 -5 meters, or even better, with advanced equipment. Differential correction requiresa second GPS receiver, a base station, collecting data at a stationary position on aprecisely known point (typically it is a surveyed benchmark). Because the physicallocation of the base station is known, a correction factor can be computed bycomparing the known location with the GPS location determined by using thesatellites.

GPS location

Geographical coordinates and elevation uses ellipsoidal reference



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Geoid

The geoid approximates mean sea level.

The shape of the ellipsoid was calculated based on the hypothetical equipotentialgravitational surface.

A significant difference exists between this mathematical model and the real object.

However, even the most mathematically sophisticated geoid can only approximatethe real shape of the earth.



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measurements and modeling the surface mathematically. Previously, there was no way toaccurately measure the geoid so it was roughly approximated by MSL. Although forpractical purposes, at the coastline the geoid and MSL surfaces are assumed to beessentially the same, at some spots the geoid can actually differ from MSL by severalmeters.

GPS has transformed how altitude at any spot is measured. GPS uses an ellipsoid

coordinate system for both its horizontal and vertical datums. An ellipsoid—or flattenedsphere—is used to represent the geometric model of the earth.

Receiver Position, Velocity, and Time

Position in XYZ is converted within the receiver to geodetic latitude, longitude andheight above the ellipsoid.

Latitude and longitude are usually provided in the geodetic datum on which GPS isbased (WGS-84). Receivers can often be set to convert to other user-requireddatums. Position offsets of hundreds of meters can result from using the wrong

datum.

Velocity is computed from change in position over time, the SV Dopplerfrequencies, or both.

Time is computed in SV Time, GPS Time, and UTC.

GPS for GIS

The "what" is the object or objects which will be mapped. These objects are

referred to as "Features", and are used to build a GIS. It is the power of GPS toprecisely locate these Features which adds so much to the utility of the GIS system.On the other hand, without Feature data, a coordinate location is of little value.

Feature Types :There are three types of Feature which can be mapped: Points,Lines and Areas.

A Point Feature is a single GPS coordinate position which is identified with aspecific Object.

A Line Feature is a collection of GPS positions which are identified with the sameObject and linked together to form a line.

An Area Feature is very similar to a Line Feature, except that the ends of the lineare tied to each other to form a closed area.

Describing Features A Feature is the object which will be mapped by the GPS system. The ability to describe a Feature in terms of a multi-layered database is essential for

successful integration with any GIS system. For example, it is possible to map the location of each house on a city block and

simply label each coordinate position as a house. However, the addition of information such as color, size, cost, occupants, etc. will

provide the ability to sort and classify the houses by these categories. These categories of descriptions for a Feature are know as Attributes.



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Attributes can be thought of as questions which are asked about the Feature. Using the example above, the Attributes of the Feature "house" would be "color",

"size", "cost" and "occupants". Logically, each question asked by the Attributes must have an answer. The answers to the questions posed by the Attributes are called Values. In the example above, an appropriate Value (answer) for the Attribute (question)

"color" may be "blue".

User Segment

Military.

Search and rescue.

Disaster relief.

Surveying.

Marine, aeronautical and terrestrial navigation.

Remote controlled vehicle and robot guidance.

Satellite positioning and tracking.

Shipping.

Geographic Information Systems (GIS). Recreation.

ieq-05global positioning system notes

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